Is every toric variety an M-variety?
Algebraic Geometry
2007-08-13 v1 Algebraic Topology
Abstract
A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in Z/2) coincides with the corresponding sum for the real part of X. It has been known for a long time that any nonsingular complete toric variety is an M-variety. In this paper we consider whether this remains true for toric varieties that are singular or not complete, and we give a positive answer when the dimension of X is less than or equal to 3.
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Cite
@article{arxiv.math/0510228,
title = {Is every toric variety an M-variety?},
author = {Frédéric Bihan and Matthias Franz and Clint McCrory and Joost van Hamel},
journal= {arXiv preprint arXiv:math/0510228},
year = {2007}
}
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13 pages